Variational Marginal Particle Filters

Background

Tensorflow implementation for AISTATS 2022 paper: Variational Marginal Particle Filters.

The differentiable particle filtering part of the codes is modified from https://github.com/JTT94/filterflow.

Dependencies

• Python 3.6.8
• Tensorflow 2.4.1
• Tensorflow-Probability 0.12.2

See requirements.txt for details.

Training Commands

Linear Gaussian State Space Models

For example, if we want to reproduce the result of Linear Gaussian SSMs with ($d_x=25$, $d_y=25$, C sparse) with $N=4$. We need to run

python -m experiment.run --d_x 25 --d_y 25 --obs sparse --n 4 --lr 0.01,0.001 --epochs 10000,10000 --algorithm 'algorithm'

where 'algorithm' is

• IWVI: ImportanceWeightedVariationalInference
• VSMC: VariationalSequentialMonteCarlo
• VMPF-BG: VariationalMarginalParticleFilterBiasedGradients
• VMPF-UG: VariationalMarginalParticleFilter

The saved model and training procedure is saved at final/LinearGaussianData/. If we want to retrieve the parameters of some saved model and continue training, the option --retrieve final/LinearGaussianData/.../ckpt-1 should be added.

To train TMC for this model and stochastic volatility models, additional option --proposal Normal4TMC should be added to the training scripts for VMPF-UG. For DPF, run python -m experiment.differentiable_particle_filter --n_particles 4 for the same comparison.

Stochastic Volatility Models

We use the same training scripts as Linear Gaussian SSM, except that additional options --proposal PriorAndNormal --dataset StochasticVolatilityData --model StochasticVolatility should be included to specify the model, proposal and dataset.

If we want to run VMPF-BG on triangular B, we need

python -m experiment.run --proposal PriorAndNormal --dataset StochasticVolatilityData --model StochasticVolatility --beta_form triangular --n 4 --lr 0.003,0.0003,0.00003,0.000003 --epochs 100000,100000,100000,100000 --algorithm VariationalMarginalParticleFilterBiasedGradients

For diagonal B, we replace 'triangular' with 'diagonal' and adjust the learning rates as well as epochs.

Deep Markov Models

Deep Markov models use multiple data instead of single data. So we use a different training code. If we want to train on JSB dataset with VMPF-BG, the following command is needed.

python -m experiment.run_multiple_data --lr 0.001,0.0001 --n 4 --dataset JSB --epochs 1000,200 --d_h 64 --algorithm VariationalMarginalParticleFilterBiasedGradientsMultipleData

Note that the name of all algorithms are added with 'MultipleData' to distinguish from single data case. And we can replace the dataset name with 'Piano-midi.de', 'Nottingham' or 'MuseData' to run on the other three datasets.

To train TMC, additional option --proposal DNN4TMC should be added to the training scripts for VMPF-UG. For DPF, run python -m experiment.dpf_multiple_data --lr 0.001,0.0001 --n_particles 4 --dataset JSB --n_iter 1000,200 --d_h 64 for the same comparison.